Question about observation equations?

Estimation ML/Bayesian estimation
1

Dear Professor Pfeifer,

I’ve read your paper A Guide to Specifying Observation Equations for the Estimation of DSGE Models, but I still got bad results (bad mode plot ) when running the Bayesian Estimation. I want to find where the mistake is. Following is the observation equations and data dealing process. Would you please give some advice? Thank you very much.

I use five observation variables, YU (output), CU (consumption), IU (investment), piU (inflation rate), RU (gross interest rate).

The model is nonlinear and I use exp form such as exp(YU) exp(CU) … in the model block. The observation equations are:

YU_ob = YU-log(YUU);
piU_ob = piU;
CU_ob = CU-log(CUU);
IU_ob = IU-log(IUU);
RU_ob = RU;

For the data of YU CU IU, I got the raw nominal data and do the seasonal adjustment, and change it to the real data, and got the log real data, and finally use the One-sided HP filter.
For the data of piU, I ffirst got raw CPI data, and then use log( CPI(t)/CPI(t-1) ).
For the data of RU, I got raw annual net interest rate, and then use log(1+Rdata/4).

Would you please tell me where could be the mistake? Thanks again.

2

Hi, Don’t you apply the log to YU, CU and IU? If not this is a problem because in your model the variables are in logarithm.

Best,
Stéphane.

3

Dear Professor Adjemian,

I so sorry that I forgot to tell the real data of Y C and I are applied log before using the One-sided HP filter.
which means:
For the data of YU CU IU, I got the raw nominal data and do the seasonal adjustment, and change it to the real data, and got the log real data and finally use the One-sided HP filter.(I change this in the original post)

Is there any other mistake in the process?

Any reply will be appreciated. Thanks.

4

The only potential problem I can see is that often you need to use

log(1+Rdata/400)

instead of

log(1+Rdata/4)

But that is easy to figure out.
The second issue may be that you have some variables like the interest rate and inflation that still have their mean in there.

5

Dear Professor Pfeifer,

The data of RU I got has already divided by 100, e.g. 4% is 0.04, so I just use log(1+0.04/4). Is this right?

For the second issue, do you mean that I should demean the data of interest rate and inflation? I’ve tried this, but the problem still not solved. The demean process was using log(1+Rdata/400) - mean(log(1+Rdata/400))
log( CPI(t)/CPI(t-1) ) - mean(log( CPI(t)/CPI(t-1) ))

and the observation equations become
piU_ob = piU-log(piUU);
RU_ob = RU-log(RUU);

Did I make any mistake?

Any reply will be appreciated. Thank you.

6

Without seeing the files that is hard to tell. Whether you have to demean depends on the rest of the model.